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Add lemmas about memory #8

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Add lemmas about memory #8

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11c8cba
Useful lemmas, mostly regarding memory
Coda-Coda Oct 1, 2024
2545bfd
Remove unneeded `aesop` Fixes build of `State.lean`
Coda-Coda Sep 27, 2024
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35 changes: 33 additions & 2 deletions Clear/Abstraction.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,7 @@ import Clear.ExecLemmas
import Clear.OutOfFuelLemmas
import Clear.JumpLemmas
import Clear.YulNotation
import Clear.Wheels

namespace Clear.Abstraction

Expand All @@ -18,7 +19,7 @@ variable {s s₀ s₁ sEnd : State}

-- | General form for relational specs (concrete and abstract).
@[aesop safe 0 unfold (rule_sets := [Clear.aesop_spec])]
def Spec (R : State → State → Prop) (s₀ s₁ : State) : Prop :=
def Spec (R : State → State → Prop) (s₀ s₁ : State) :=
match s₀ with
| OutOfFuel => ❓ s₁
| Checkpoint c => s₁.isJump c
Expand All @@ -31,6 +32,30 @@ lemma Spec_ok_unfold {P : State → State → Prop} :
unfold Spec
aesop

-- | Specs that are somewhat pure
@[aesop safe 0 unfold (rule_sets := [Clear.aesop_spec])]
def PureSpec (R : State → State → Prop) : State → State → Prop :=
Spec (R ∩ (preserved on evm))

lemma PureSpec_ok_unfold {P : State → State → Prop} :
∀ {s s' : State}, s.isOk → ¬ ❓ s' → PureSpec P s s' → (P ∩ (preserved on evm)) s s' := by
intros s s' h h'
unfold PureSpec Spec
aesop

-- | Specs for code that might result in hash collision
@[aesop safe 0 unfold (rule_sets := [Clear.aesop_spec])]
def CollidingSpec (R : State → State → Prop) (s₀ s₁ : State) : Prop :=
if s₀.evm.hash_collision
then ❓ s₁
else ¬ s₁.evm.hash_collision → Spec R s₀ s₁

lemma CollidingSpec_ok_unfold {P : State → State → Prop} :
∀ {s s' : State}, s.isOk → ¬ ❓ s' → ¬ s'.evm.hash_collision → CollidingSpec P s s' → P s s' := by
intros s s' h h' h''
unfold CollidingSpec Spec
aesop

open Lean Elab Tactic in
elab "clr_spec" "at" h:ident : tactic => do
evalTactic <| ← `(tactic| (
Expand All @@ -46,6 +71,12 @@ lemma not_isOutOfFuel_Spec (spec : Spec R s₀ s₁) (h : ¬ isOutOfFuel s₁) :
intros hs₀
aesop_spec

-- | No hash collision propagates backwards through specs.
-- lemma not_hashCollision_Spec
-- (spec : CollidingSpec R s₀ s₁) (h : ¬ s₁.evm.hasHashCollision) : ¬ s₀.evm.hasHashCollision := by
-- intros hs₀
-- aesop_spec

-- ============================================================================
-- TACTICS
-- ============================================================================
Expand Down Expand Up @@ -151,7 +182,7 @@ elab "clr_funargs" "at" h:ident : tactic => do
simp only [multifill_cons, multifill_nil', isOk_insert, isOk_Ok, isOutOfFuel_Ok,
not_false_eq_true, imp_false, Ok.injEq, and_imp, forall_apply_eq_imp_iff₂,
forall_apply_eq_imp_iff] at $h:ident
repeat (rw [←State.insert] at $h:ident)
repeat (rw [←State.insert] at $h:ident)
))

end Clear
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